Lattice computation of the nucleon scalar quark contents at the physical point

S. Durr (1, 2) , Z. Fodor (1, 2) , C. Hoelbling (2) , S. D. Katz (3) , S. Krieg (1, 2) , Laurent Lellouch (4, 5) , T. Lippert (2, 1) , Thibaut Métivet (4, 5, 6) , A. Portelli (4, 5, 7) , K. K. Szabo (2, 1) , C. Torrero (4, 5) , B. C. Toth (2) , L. Varnhorst (2)

1 JSC - Jülich Supercomputing Centre
2 Theoretische Teilchenphysik
3 Departement for Theoretical Physics
4 CPT - Centre de Physique Théorique - UMR 7332
5 CPT - E1 Physique des particules
6 DPHN - Département de Physique Nucléaire (ex SPhN)
7 Edin. - University of Edinburgh

We present a calculation of the $u$, $d$ and $s$ scalar quark contents of nucleons in QCD. Our calculation is based on $47$ lattice QCD ensembles with $N_f=2+1$ dynamical sea quarks, $5$ lattice spacings down to $0.054\,\text{fm}$, lattice sizes up to $6\,\text{fm}$ and pion masses down to $120\,\text{MeV}$. Using the Feynman-Hellmann theorem, we obtain $f_{ud}^N = 0.0405(40)(35)$ and $f_{s}^N=0.113(45)(40)$, which translates into $\sigma_{\pi N}=38(3)(3)\,\text{MeV}$, $\sigma_{sN}=105(41)(37)\,\text{MeV}$ and $y_N=0.20(8)(8)$ for the sigma terms and the related ratio, where the first errors are statistical and the second an estimate of the systematics. Using isospin relations and our recent result for the QCD contribution to the $n$-$p$ mass difference, we also compute the individual up and down quark contents of the proton and neutron. We obtain $f_u^p=0.0139(13)(12)$, $f_d^p=0.0253(28)(24)$, $f_u^n=0.0116(13)(11)$ and $f_d^n=0.0302(28)(25)$.

Domaines: Physique des Hautes Energies - Réseau [hep-lat]; Physique des Hautes Energies - Phénoménologie [hep-ph]

S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, et al.. Lattice computation of the nucleon scalar quark contents at the physical point. Physical Review Letters, 2016, 116 (17), pp.172001. ⟨10.1103/PhysRevLett.116.172001⟩. ⟨hal-01259005⟩